| Label |
Class |
Class size |
Class degree |
Base field |
Field degree |
Field signature |
Conductor |
Conductor norm |
Discriminant norm |
Root analytic conductor |
Bad primes |
Rank |
Torsion |
CM |
CM |
Sato-Tate |
$\Q$-curve |
Base change |
Semistable |
Potentially good |
Nonmax $\ell$ |
mod-$\ell$ images |
$Ш_{\textrm{an}}$ |
Tamagawa |
Regulator |
Period |
Leading coeff |
j-invariant |
Weierstrass coefficients |
Weierstrass equation |
| 300.1-a2 |
300.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
300.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \) |
$0.64414$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/12\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
✓ |
|
$2, 3$ |
2B, 3B.1.1[2] |
$1$ |
\( 2^{3} \cdot 3 \) |
$1$ |
$3.882870421$ |
0.747258760 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a\) , \( 1\) , \( a - 2\) , \( 2\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-a{x}^{2}+\left(a-2\right){x}+2$ |
| 7500.1-b2 |
7500.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
7500.1 |
\( 2^{2} \cdot 3 \cdot 5^{4} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{14} \) |
$1.44034$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/4\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{5} \) |
$1$ |
$0.776574084$ |
1.793421026 |
\( \frac{357911}{2160} \) |
\( \bigl[1\) , \( 1\) , \( 1\) , \( 37\) , \( 281\bigr] \) |
${y}^2+{x}{y}+{y}={x}^{3}+{x}^{2}+37{x}+281$ |
| 19200.1-e2 |
19200.1-e |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
19200.1 |
\( 2^{8} \cdot 3 \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{6} \cdot 5^{2} \) |
$1.82190$ |
$(-2a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
✓ |
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.970717605$ |
2.241776282 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( -1\) , \( 0\) , \( 24\) , \( -144\bigr] \) |
${y}^2={x}^{3}-{x}^{2}+24{x}-144$ |
| 44100.1-b2 |
44100.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.1 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (-3a+1), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.847311791$ |
1.956782763 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( a + 1\) , \( 0\) , \( -20 a - 14\) , \( 100 a - 228\bigr] \) |
${y}^2+\left(a+1\right){x}{y}={x}^{3}+\left(a+1\right){x}^{2}+\left(-20a-14\right){x}+100a-228$ |
| 44100.3-b2 |
44100.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
44100.3 |
\( 2^{2} \cdot 3^{2} \cdot 5^{2} \cdot 7^{2} \) |
\( 2^{8} \cdot 3^{12} \cdot 5^{2} \cdot 7^{6} \) |
$2.24289$ |
$(-2a+1), (3a-2), (2), (5)$ |
0 |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1$ |
$0.847311791$ |
1.956782763 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -a - 1\) , \( 1\) , \( 13 a + 22\) , \( -135 a - 115\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(13a+22\right){x}-135a-115$ |
| 50700.1-b2 |
50700.1-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.1 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (-4a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.547744533$ |
$1.076914492$ |
2.724511424 |
\( \frac{357911}{2160} \) |
\( \bigl[a + 1\) , \( -1\) , \( 1\) , \( -23 a + 10\) , \( 81 a + 38\bigr] \) |
${y}^2+\left(a+1\right){x}{y}+{y}={x}^{3}-{x}^{2}+\left(-23a+10\right){x}+81a+38$ |
| 50700.3-b2 |
50700.3-b |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
50700.3 |
\( 2^{2} \cdot 3 \cdot 5^{2} \cdot 13^{2} \) |
\( 2^{8} \cdot 3^{6} \cdot 5^{2} \cdot 13^{6} \) |
$2.32248$ |
$(-2a+1), (4a-3), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$0.547744533$ |
$1.076914492$ |
2.724511424 |
\( \frac{357911}{2160} \) |
\( \bigl[a\) , \( -a\) , \( 1\) , \( 22 a - 12\) , \( -81 a + 119\bigr] \) |
${y}^2+a{x}{y}+{y}={x}^{3}-a{x}^{2}+\left(22a-12\right){x}-81a+119$ |
| 57600.1-a2 |
57600.1-a |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{12} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.427139629$ |
$0.560444070$ |
3.694265501 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( -a - 1\) , \( 0\) , \( 72 a\) , \( -864 a + 432\bigr] \) |
${y}^2={x}^{3}+\left(-a-1\right){x}^{2}+72a{x}-864a+432$ |
| 57600.1-p2 |
57600.1-p |
$8$ |
$12$ |
\(\Q(\sqrt{-3}) \) |
$2$ |
$[0, 1]$ |
57600.1 |
\( 2^{8} \cdot 3^{2} \cdot 5^{2} \) |
\( 2^{32} \cdot 3^{12} \cdot 5^{2} \) |
$2.39775$ |
$(-2a+1), (2), (5)$ |
$1$ |
$\Z/2\Z$ |
$\textsf{no}$ |
|
$\mathrm{SU}(2)$ |
✓ |
|
|
|
$2, 3$ |
2B, 3B[2] |
$1$ |
\( 2^{3} \) |
$1.427139629$ |
$0.560444070$ |
3.694265501 |
\( \frac{357911}{2160} \) |
\( \bigl[0\) , \( a + 1\) , \( 0\) , \( 72 a\) , \( 864 a - 432\bigr] \) |
${y}^2={x}^{3}+\left(a+1\right){x}^{2}+72a{x}+864a-432$ |
*The rank, regulator and analytic order of Ш are
not known for all curves in the database; curves for which these are
unknown will not appear in searches specifying one of these
quantities.
